A manufacturer has developed a new fishing line which he claims has a mean breaking strength of greater than 15 kilograms. A random sample of 50 lines are selected and tested and were found to have an average of 15.1 kilograms with a standard deviation of 0.5 kilograms. Can it be concluded at line is greater than 15 kilograms.

A soft drink dispensing machine is said to be out of control if the variance of the contents exceeds 1.15 deciliters. If a random sample of 25 drinks from this machine has a variance of 2.03 deciliters . Conduct an appropriate hypothesis test to determine at the 0.05 level of significance if the machine is out of control? Assume that the contents are approximately normally distributed.